question_answer

A path of uniform width runs round the inside of a rectangular field 38 m long and 32 m wide. If the path occupies 600, then the width of the path is

A)  30 m               

B)  5 m

C)  18.75 m                      

D)  10 m

Correct Answer: B

Solution :

Let the width of path be x m.

Area of rectangular field \[=38\times 32=1216\,\,{{m}^{2}}\]

Area of rectangular field without path

\[=(38-2x)(32-2x)\]

\[=1216-64x-76x+4{{x}^{2}}\]

\[=1216-140x+4{{x}^{2}}\]

\[\therefore \]Area of the path \[=1216-1216+140x-4{{x}^{2}}\]

\[=140x-4{{x}^{2}}\]

\[\therefore \]      \[140x-4{{x}^{2}}=600\]

\[\Rightarrow \]\[4{{x}^{2}}-140x+600=0\]

\[\Rightarrow \]\[{{x}^{2}}-35x+150=0\]

\[\Rightarrow \]\[{{x}^{2}}-30x-5x+150=0\]

\[\Rightarrow \]\[x\,\,(x-30)-5\,\,(x-30)=0\]

\[\Rightarrow \]\[(x-5)\,\,(x-30)=0\]

\[\Rightarrow \]\[x=5\]as\[x\ne 30\]